Question

Heavy Metal Corporation (HMC) is a leader in ship building industry. It is considering building a new shipyard facility. Currently, there is no outstanding debt in company's balance sheet. The new project will be financed by issuing new equity only. We have the following information about the company's equity and the stock market. The company's share is now trading at $100. The company paid dividend of $16 per sharq last year. The market expects that the comnany will maintain this dividend amount in the foreseeable future. The beta (B) of the company's shares is 1.25. The expected market return is 13% and the yield to maturity of government debt is 4%. a. Compute the cost of equity by the Capital Asset Pricing Model (CAPM). b. Compute the cost of equity by the dividend growth model (DGM). c. As the CFO of the company, you find that you have different values of the cost of equity by CAPM and DGM. How do you determine the cost of equity? Explain. d. Discuss the advantages and disadvantages of CAPM and DGM. e. The project manager of HMC suggests that the company should use more debt rather than equity to finance this project since debt is cheaper than equity. Will you take this advice? Explain your answer by using M&M capital structure theory.

Answer 1

a) Computation of Cost of Equity by Capital Asset Pricing Model (CAPM)

Cost of Equity is the rate of return a shareholder requires for investing equity into a business. The rate of return an investor requires is based on the level of risk associated with the investment, which is measured as the historical volatility of returns. A firm uses cost of equity to assess the relative attractiveness of investments, including both internal projects and external acquisition opportunities.

The cost of equity can be calculated by using the CAPM (Capital Asset Pricing Model) or Dividend Capitalization Model (for companies that pay out dividends).

1. CAPM (Capital Asset Pricing Model)

CAPM takes into account the riskiness of an investment relative to the market.

CAPM Formula:

E(R_i) = R_f + β_i * [E(R_m) – R_f]

Where:

E(R_i) = Expected return on asset i

R_f = Risk-free rate of return

β_i = Beta of asset i

E(R_m) = Expected market return

Here, R_f = Yield to maturity of govt. debt = 4% =0.04
E(R_m) = 13% = 0.13
Beta = 1.25

Therefore, E(R_i) = 0.04 + 1.25 * (0.13 - 0.04) = 0.04 + 1.25 * 0.09 = 0.04 + 0.1125 = 0.1525
E(R_i) = 0.1525 = 15.25%

ERP (Equity Risk Premium) = E(R_m) – R_f

Therefore, we can also say, cost of Equity or  E(R_i) = R_f + β_i*ERP

Hence, Cost of equity of Heavy Metal Corporation as per the CAPM model is 15.25 %

The company with the highest beta sees the highest cost of equity and vice versa. It makes sense because investors must be compensated with a higher return for the risk of more volatility (a higher beta).

b)Computation of Cost of Equity by the Dividend Growth Model

The Dividend Capitalization Model only applies to companies that pay dividends, and it also assumes that the dividends will grow at a constant rate. The model does not account for investment risk to the extent that CAPM does (since CAPM requires beta).

Dividend Capitalization Formula:

R_e = (D₁ / P₀) + g

Where:

R_e = Cost of Equity

D₁ = Dividends/share next year

P₀ = Current share price

g = Dividend growth rate

Dividend Growth = (D_t/D_t-1) – 1

Where:

D_t = Dividend payment of year t

D_t-1 = Dividend payment of year t-1 (one year before year t)

Since the company is giving same amt. of dividend every year , the dividend growth rate is zero.

As, D_t = $16, D_t-1 = $16, Therefore , Dividend Growth or g = 16 /16 - 1 = 1-1 = 0

Since, here, D₁ = $16, P₀ = $100, g = 0

Therefore Cost of Equity or R_e = (D₁ / P₀) + g = 16/100 + 0 = 0.16
Cost of Equity of Heavy Metal Corporation = 0.16 or 16%.

c) Since, our estimates for cost for equity under both the models are close, this adds credibility to our estimate. Financial analysts frequently use more than one models to estimate any statistic to obtain a range of values. Hence, as a CFO of a company , we need to calculate the cost of equity using two or more available formulas.

We are also required to calculate the Cost of retained earnings/cost of internal equity.

The retained earnings are a component of equity, and, therefore, the cost of retained earnings (internal equity) is equal to the cost of equity. Dividends (earnings that are paid to investors and not retained) are a component of the return on capital to equity holders, and influence the cost of capital through that mechanism.

Cost of internal equity = [(next year's dividend per share/(current market price per share - flotation costs)] + growth rate of dividends)].

There are many other methods also used to compute a cost of equity which are running a regression analysis, multi-factor model, survey method etc.
A multi-factor model is a financial model that employs multiple factors in its calculations to explain market phenomena and/or equilibrium asset prices. The multi-factor model can be used to explain either an individual security or a portfolio of securities. It does so by comparing two or more factors to analyze relationships between variables and the resulting performance.

d) Advantages of CAPM & DGM

The dividend capitalization model can be used to calculate the cost of equity, but it requires that a company pays dividends. The calculation is based on future dividends. The theory behind the equation is the company's obligation to pay dividends is the cost of paying shareholders and therefore the cost of equity. This is a limited model in its interpretation of costs.

The capital asset pricing model, however, can be used on any stock, even if the company does not pay dividends. That said, the theory behind CAPM is more complicated. The theory suggests the cost of equity is based on the stock's volatility and level of risk compared to the general market.
In the CAPM equation, the risk-free rate is the rate of return paid on risk-free investments such as Treasuries. Beta is a measure of risk calculated as a regression on the company's stock price. The higher the volatility, the higher the beta and relative risk compared to the general market. The market rate of return is the average market rate. In general, a company with a high beta, that is, a company with a high degree of risk will have a higher cost of equity.

It is important to note that the cost of equity can mean two different things, depending on who's using it. Investors use it as a benchmark for an equity investment, while companies use it for projects or related investments.

Dividend discount model for estimation of cost of equity is useful only when the stock is dividend-paying. But there are many stocks which do not pay dividends. In such situations, the capital asset pricing model and some other more advanced models are used.

Advantages of the CAPM

The CAPM has several advantages over other methods of calculating required return, explaining why it has been popular for more than 40 years:

• It considers only systematic risk, reflecting a reality in which most investors have diversified portfolios from which unsystematic risk has been essentially eliminated.
• It is a theoretically-derived relationship between required return and systematic risk which has been subject to frequent empirical research and testing.
• It is generally seen as a much better method of calculating the cost of equity than the dividend growth model (DGM) in that it explicitly considers a company’s level of systematic risk relative to the stock market as a whole.
• It is clearly superior to the WACC in providing discount rates for use in investment appraisal.

Disadvantages of the CAPM

The CAPM suffers from several disadvantages and limitations.

Assigning values to CAPM variables

To use the CAPM, values need to be assigned to the risk-free rate of return, the return on the market, or the equity risk premium (ERP), and the equity beta.

The yield on short-term government debt, which is used as a substitute for the risk-free rate of return, is not fixed but changes regularly with changing economic circumstances. A short-term average value can be used to smooth out this volatility.

Finding a value for the equity risk premium (ERP) is more difficult. The return on a stock market is the sum of the average capital gain and the average dividend yield. In the short term, a stock market can provide a negative rather than a positive return if the effect of falling share prices outweighs the dividend yield. It is therefore usual to use a long-term average value for the ERP, taken from empirical research, but it has been found that the ERP is not stable over time. In the UK, an ERP value of between 3.5% and 4.8% is currently seen as reasonable. However, uncertainty about the ERP value introduces uncertainty into the calculated value for the required return.

Beta values are now calculated and published regularly for all stock exchange-listed companies. The problem here is that uncertainty arises in the value of the expected return because the value of beta is not constant, but changes over time.

Comparing the dividend growth model and CAPM

The dividend growth model allows the cost of equity to be calculated using empirical values readily available for listed companies. Measure the dividends, estimate their growth (usually based on historical growth), and measure the market value of the share. Put these amounts into the formula and we have an estimate of the cost of equity.

However, the model gives no explanation as to why different shares have different costs of equity. Why might one share have a cost of equity of 15% and another of 20%? The reason that different shares have different rates of return is that they have different risks, but this is not made explicit by the dividend growth model. That model simply measures what’s there without offering an explanation.We should note that a business cannot alter its cost of equity by changing its dividends. The equation:

R_e = D₀(1 + g) / P₀ + g

might suggest that the rate of return would be lowered if the company reduced its dividends or the growth rate. That is not so. All that would happen is that a cut in dividends or dividend growth rate would cause the market value of the company to fall to a level where investors obtain the return they require.

The CAPM explains why different companies give different returns. It states that the required return is based on other returns available in the economy (the risk free and the market returns) and the systematic risk of the investment – its beta value. Not only does CAPM offer this explanation, it also offers ways of measuring the data needed. The risk free rate and market returns can be estimated from economic data. So too can the beta values of listed companies. It is, in fact, possible to buy books giving beta values and many investment websites quote investment betas.

When an investment and the market is in equilibrium, prices should have been adjusted and should have settled down so that the return predicted by CAPM is the same as the return that is measured by the dividend growth model.

It is to be noted that although both of these approaches give you the cost of equity, they do not give you the weighted average cost of capital other than in the very special circumstances when a company has only equity in its capital structure.

e) The Modigliani and Miller approach to capital structure theory, devised in the 1950s, advocates the capital structure irrelevancy theory. This suggests that the valuation of a firm is irrelevant to the capital structure of a company. Whether a firm is highly leveraged or has a lower debt component has no bearing on its market value. Rather, the market value of a firm is solely dependent on the operating profits of the company.
The capital structure of a company is the way a company finances its assets. A company can finance its operations by either equity or different combinations of debt and equity. The capital structure of a company can have a majority of the debt component or a majority of equity, or an even mix of both debt and equity.
The Modigliani and Miller Approach further states that the market value of a firm is affected by its operating income, apart from the risk involved in the investment. The theory stated that the value of the firm is not dependent on the choice of capital structure or financing decisions of the firm.
ASSUMPTIONS OF MODIGLIANI AND MILLER APPROACH

• There are no taxes.
• Transaction cost for buying and selling securities, as well as the bankruptcy cost, is nil.
• There is a symmetry of information. This means that an investor will have access to the same information that a corporation would and investors will thus behave rationally.
• The cost of borrowing is the same for investors and companies.
• There is no floatation cost, such as an underwriting commission, payment to merchant bankers, advertisement expenses, etc.
• There is no corporate dividend tax.

The Modigliani and Miller Approach indicates that the value of a leveraged firm (a firm that has a mix of debt and equity) is the same as the value of an unleveraged firm (a firm that is wholly financed by equity) if the operating profits and future prospects are same. That is, if an investor purchases shares of a leveraged firm, it would cost him the same as buying the shares of an unleveraged firm.

MODIGLIANI AND MILLER APPROACH: TWO PROPOSITIONS WITHOUT TAXES

PROPOSITION 1

With the above assumptions of “no taxes”, the capital structure does not influence the valuation of a firm. In other words, leveraging the company does not increase the market value of the company. It also suggests that debt holders in the company and equity shareholders have the same priority, i.e., earnings are split equally amongst them.

PROPOSITION 2

It says that financial leverage is in direct proportion to the cost of equity. With an increase in the debt component, the equity shareholders perceive a higher risk to the company. Hence, in return, the shareholders expect a higher return, thereby increasing the cost of equity. A key distinction here is that Proposition 2 assumes that debt shareholders have the upper hand as far as the claim on earnings is concerned. Thus, the cost of debt reduces.

MODIGLIANI AND MILLER APPROACH: PROPOSITIONS WITH TAXES (THE TRADE-OFF THEORY OF LEVERAGE)

The Modigliani and Miller Approach assumes that there are no taxes, but in the real world, this does not happen. Most companies are tax companies. This theory recognizes the tax benefits accrued by interest payments. The interest paid on borrowed funds is tax deductible. However, the same is not the case with dividends paid on equity. In other words, the actual cost of debt is less than the nominal cost of debt due to tax benefits. The trade-off theory advocates that a company can capitalize its requirements with debts as long as the cost of distress, i.e., the cost of bankruptcy, exceeds the value of the tax benefits. Thus, the increased debts, until a given threshold value, will add value to a company.

This approach with corporate taxes does acknowledge tax savings and thus infers that a change in the debt-equity ratio has an effect on the WACC (Weighted Average Cost of Capital). This means that the higher the debt, the lower the WACC.

Determinants of Capital Structure

Debt ratios are related to industry factors and expected growth, non-debt tax shields, profitability, volatility of earnings, business risk, capital market conditions, government policy, debt service capacity, size of firm etc

M & M , offer the most convincing argument in support of their opinion that, there does not exist an optimal capital structure at any stage and the market value of a firm is not influenced in any way by the leverage factor Thus they in their famous propositions they declare to the world that the value of a corporation is dependent upon its underlying profitability and risk and does not vary with the relevant changes in the firm's capital structure. In proposition I, M & M argue that, for firms in the same risk class, the total market value is independent of the debt equity combination, and is given by capitalizing the expected net operating income at a discount rate appropriate to its risk class Alternatively, proposition I holds that, the average cost of capital to any firm is completely independent of its capital structure and is equal to the capitalization rate of a pure equity stream of its class.
Derived from proposition I, M & M provide a formula in proposition II to determine the cost of equity capital which states that, the required rate of return on equity for a levered firm increases in direct proportion to the debt to equity ratio of the company, with the debt ratio being determined by the market values of the companies securities.Any gains from using cheaper debt capital would be offset by the correspondingly higher cost of the now riskier equity capital.
The cut-off point for the investment in the firm will in all cases be completely unaffected by the security issued to finance the investment, implying that whether you use debt or equity to finance an investment will not affect its profitability This proposition emphasizes the point that, investment and financing decisions are independent because the average cost of capital is not affected by the financing decision.

The reasoning behind the M & M theorems is their arbitrage argument that, in well functioning markets two investments that offer the same payoff must have the same cost.

Hence, using M&M approach, we can say that using more debt as compared to equity does'nt make any difference.